When looking for the best stocks to buy, most investors typically search for new opportunities, meaning companies which they do not already own in their portfolio. Similarly, investors tend to only increase their positions in companies which are down in price, buying at lower levels and reducing the average purchase price. This can be the right thing to do on many occasions. However, you need to keep an open mind when it comes to increasing positions in your best performing stocks, as this can be a powerful strategy for superior returns.

Timeless investment advice from Warren Buffett and Peter Lynch
Warren Buffett is arguably the most successful investor in history, and he also has an amazing talent to explain important investing concepts in simple and powerful terms. The Oracle of Omaha believes that the smart thing to do is sticking to your best investment ideas for the true long-term, and he even quoted Peter Lynch on this matter in his 1988 shareholder letter:

When we own portions of outstanding businesses with outstanding managements, our favorite holding period is forever. We are just the opposite of those who hurry to sell and book profits when companies perform well but who tenaciously hang on to businesses that disappoint. Peter Lynch aptly likens such behavior to cutting the flowers and watering the weeds. 

Elaborating on this subject, Peter Lynch explained how the mathematics of investing returns mean that sticking to your winners for the long-term can make all the difference in the world. You don't really need to pick a lot of winning stocks to thrive in the market over the years -- the key is having a few big winners and letting them run for as long as possible.

One of the oldest sayings on Wall Street is "Let your winners run, and cut your losers." It's easy to make a mistake and do the opposite, pulling out the flowers and watering the weeds. Warren Buffett quoted me on this point in one of his famous annual reports (as thrilling to me as getting invited to the White House). If you're lucky enough to have one golden egg in your portfolio, it may not matter if you have a couple of rotten ones in there with it.

Let's say you have a portfolio of six stocks. Two of them are average, two of them are below average, and one is a real loser. But you also have one stellar performer. Your Coca-Cola(NYSE:KO), your Gillette. A stock that reminds you why you invested in the first place. In other words, you don't have to be right all the time to do well in stocks. If you find one great growth company and own it long enough to let the profits run, the gains should more than offset  mediocre results from other stocks in your portfolio.

How to find big winners
There is not such a thing as a single and infallible method to find superior investments, however, many of the most successful companies share some important traits. If you have to pick one factor above all, competitive strength is arguably the most relevant aspect to consider.

Coca-Cola is one of the most iconic Warren Buffett stocks and also an amazing winner over the long-term. Its main strength is not the secretly warded Coca-Cola formula but its tremendous brand recognition. Coca-Cola is the most popular name in soft drinks by a wide margin, and the company owns a global portfolio featuring 20 different brands which produce over $1 billion each in retail revenue.

Over the last several years, Coca-Cola has adapted to changing consumer habits, putting an increased focus on products such as water, juice, and tea in order to better fit consumer needs for healthier choices. No company is completely immune to the competition, and it is always important to be flexible enough to stay in touch with changing consumer demand. But when a company such as Coca-Cola has those kinds of strengths and management plays its cards well, chances are investors will be handsomely rewarded over the long-term. 

As Warren Buffett explained during Coca-Cola's annual shareholder meeting in April of 2013, the Oracle of Omaha has never sold a single share of the company, and he is not planning to do so anytime soon. In his own words:

We've never sold a share of Coca-Cola stock, and I wouldn't think of selling a share. I'm the kind of guy who likes to bet on sure things. No business has ever failed with happy customers ... and you're selling happiness.

You don't need to pick many big winners to do well in the market over time. All it takes is finding a few exceptional businesses and holding on to them for years or even better, decades. You don't have to take my word for it -- you can just see what Warren Buffett or Peter Lynch have to say about it.